【正文】
urier series of the acceleration history. Examination of the quasistatic stiffness matrix of Eq. 6 throughout the residual oscillationfree maneuver indicates only slight changes in the quasistatic natural frequencies of the load. Specifically, the 山東建筑大學(xué)畢業(yè)設(shè)計(jì)(或畢業(yè)論文,二選一)外文文獻(xiàn)及譯文 5 nominal (nonrotating)natural frequency in both radial and tangential directions is Hz .The initial acceleration pulse, with zero velocity, results in a slight increase of this frequency. However, the softening effect of the angular velocity during the maneuver causes the quasistatic natural frequency to decrease to Hz at the halfperiod of the maneuver. This change in quasistatic natural frequency is symmetric in time about the halfperiod. Fig. 12 shows a 20term Fourier sine series expansion of the input acceleration history. The first 5 coefficients of the jib angle history, obtained from integrating the acceleration history, are given in Table 3. Finally, some mention of the robustness of this technique is in order. It is expected that the performance of the system will suffer due to inaccuracies of the model. Sensitivity analyses indicate that the most important model parameter is the loadline length. Small errors in this quantity can lead to residual vibration, whereas similar errors in jib length can be tolerated without significant degradation of performance. Sensitivity of the response due to the discontinuous nature of the acceleration profile can be reduced by using a smoothed profile such as a versine function. This technique has been used for vibration suppression of a flexible rod, and is applicable here. l2 4. SUMMARY A method for generating residual oscillation free maneuvers for a rotary jib crane has been presented. This method uses the model of the system in conjunction with a numerical optimization process to generate parameters describing the jib angular acceleration profile. Maneuvers obtained using this procedure were experimentally verified demonstrating not only the usefulness of this method but also the ability to accurately simulate such a system. The input profiles were also shown to purposely excite the quasistatic frequencies of the payload in order to decrease the operating time of the jib crane (., decrease construction costs). 5. ACKKNOWLEDGMENTS This work performed at Sandia National Laboratories is supported by the U S Department of Energy under contract . 6. REFERENCES 山東建筑大學(xué)畢業(yè)設(shè)計(jì)(或畢業(yè)論文,二選一)外文文獻(xiàn)及譯文 6 1. . Auernig and H. Troger, “Time Optimal Control of Overhead Cranes with Hoisting of the Load,” Automatica, Vol. 23,No. 4 pp. 437447, 1987. , 2. . Moustafa and . Ebeid, “Nonlinear Modeling and Control of Overhead Crane Load Sway,” Journal of Dynamic Systems, Measurement, and Control, Vol. 110,pp. 266271,1988. 3. . Ebeid, . Moustafa and . EmaraShabaik, “Electromechanical Modelling of Overhead Cranes,” International J o u m l of Systems Science, Vol. 23,No. 12,1992. 4. M. Fliess, J. Levine P. Rouchon, “A SimplifiedApproach of Crane Control via a Generalized StateSpace Model,” IEEE Proceedings of the 30th Coilferenceon Decision and